Odds & Ends

Introducing Probability & Decision with a Visual Emphasis

Jonathan Weisberg

Preface

This textbook is for introductory philosophy courses on probability and inductive logic. It is based on a typical such course I teach at the University of Toronto, where we offer “Probability & Inductive Logic” in the second year, alongside the usual deductive logic intro.\(\,\)

The book assumes no deductive logic. The early chapters introduce the little that’s used. In fact almost no formal background is presumed, only very simple high school algebra.

Several well known predecessors inspired and shaped this book. Brian Skyrms’ Choice & Chance and Ian Hacking’s An Introduction to Probability and Inductive Logic were especially influential. Both texts are widely used with good reason—they are excellent. I’ve taught both myself many times, with great success. But this book blends my favourite aspects of each, organizing them in the sequence and style I prefer.

I hope this book also offers more universal benefits:

It is open access, hence free.

It’s also open source, so other instructors can modify it to their liking.

It’s available in both PDF and HTML. So it can be read comfortably on a range of devices, or printed.

It emphasizes visual explanations and techniques, to make the material more approachable.

It livens up the text with hyperlinks, images, and margin notes that highlight points of history and curiosity. I also hope to add some animations and interactive tools soon.

The book is divided into three main parts. The first explains the basics of logic and probability, the second covers basic decision theory, and the last explores the philosophical foundations of probability and statistics. This last, philosophical part focuses on the Bayesian and frequentist approaches.

A “cheat sheet” summarizing key definitions and formulas appears in AppendixA. Further appendices cover the axiomatic construction of probability theory, Hume’s problem of induction, and Goodman’s new ridle of induction.

I usually get a mix of students in my course, with different ideological inclinations and varying levels of background. For some the technical material is easy, even review. For others, a healthy skepticism about scientific methods and discourses comes naturally. My goal is to get these students all more or less on the same page.

By the end of the course, students with little formal background have a bevy of tools for thinking about uncertainty. They can understand much more of the statistical and scientific discourse they encounter. And hopefully they have a greater appreciation for the value of formal methods. Students who already have strong formal tools and skills will, I hope, better understand their limitations. I want them to understand why these tools leave big questions open—not just philosophically, but also in very pressing, practical ways.

The book was made with the bookdown package created by Yihui Xie. It’s a wonderful tool, built on a bunch of other technologies I love, especially the R programming language and the pandoc conversion tool created by philosopher John MacFarlane. The book’s visual style emulates the famous designs of Edward Tufte, thanks to more software created by Yihui Xie, J. J. Allaire, and many others who adapted Tufte’s designs to HTML and PDF (via LaTeX).

If it weren’t for these tools, I never would have written this book. It wouldn’t have been possible to create one that does all the things this book is meant to do. I also owe inspiration to Kieran Healy’s book Data Visualization: A Practical Introduction, which uses the same suite of tools. It gave me the idea to use those tools for an updated, open, and visually enhanced rendition of the classic material from Skyrms and Hacking.

Finally, I’m indebted to several teaching assistants and students who helped with earlier drafts. Thanks especially to Liang Zhou Koh and Meagan Phillips, who contributed several exercises; to Soroush Marouzi and Daniel Munro, who worked out the kinks during the first semester the book was piloted; and to the students in that course, who bore with us, and contributed several corrections of their own.